as seen in [1]} is often considered instead.
Replacing the \(\ell _0\) -norm with the convex, sparsity inducing \(\ell _1\) -norm results in the basis persuit denoising problem, presented as in [2]}:
\(\min _x \ \frac{1}{2} \left\Vert Ax - \overline{b}\right\Vert ^2_2 + \rho \left\Vert x\right\Vert _1 .\) 
